Iterative-Free Program Analysis Mizuhito Ogawa†∗ Zhenjiang Hu‡∗ Isao Sasano†
[email protected] [email protected] [email protected] †Japan Advanced Institute of Science and Technology, ‡The University of Tokyo, and ∗Japan Science and Technology Corporation, PRESTO Abstract 1 Introduction Program analysis is the heart of modern compilers. Most control Program analysis is the heart of modern compilers. Most control flow analyses are reduced to the problem of finding a fixed point flow analyses are reduced to the problem of finding a fixed point in a in a certain transition system, and such fixed point is commonly certain transition system. Ordinary method to compute a fixed point computed through an iterative procedure that repeats tracing until is an iterative procedure that repeats tracing until convergence. convergence. Our starting observation is that most programs (without spaghetti This paper proposes a new method to analyze programs through re- GOTO) have quite well-structured control flow graphs. This fact cursive graph traversals instead of iterative procedures, based on is formally characterized in terms of tree width of a graph [25]. the fact that most programs (without spaghetti GOTO) have well- Thorup showed that control flow graphs of GOTO-free C programs structured control flow graphs, graphs with bounded tree width. have tree width at most 6 [33], and recent empirical study shows Our main techniques are; an algebraic construction of a control that control flow graphs of most Java programs have tree width at flow graph, called SP Term, which enables control flow analysis most 3 (though in general it can be arbitrary large) [16].